### Magnetic Flux in Cylindrical Coordinates**Problem Statement:**In cylindrical coordinates, the magnetic field is given by:\[ B = \left( \frac{4}{r} \right) \hat{\phi} \text{ T} \]Determine the magnetic flux \(\Phi\) crossing the plane surface given by:\[ 0.5 \leq r \leq 2.5 \, \text{m} \]and \[ 0 \leq z \leq 2.0 \, \text{m} \]**Steps to Solve:**1. Identify the bounds of the integration in \(r\) and \(z\).2. Recognize that the magnetic field is radially dependent, and it's directed along the \(\hat{\phi}\) direction.3. Integrate the magnetic field over the specified surface area to find the magnetic flux \(\Phi\).**Explanation:**- In cylindrical coordinates, the given magnetic field varies with \(r\) and is independent of \(z\) and \(\phi\).- The problem encompasses integrating over the surface bounded in \(r\) from 0.5 m to 2.5 m and in \(z\) from 0 m to 2 m.Understanding this problem involves calculating the magnetic flux by setting up appropriate integrals over the defined bounds. The magnetic field component in the \(\hat{\phi}\) direction and its dependence on \(r\) must be considered carefully while performing the integration.**Example of Integral Setup:**\[ \Phi = \int_{0}^{2.0} \int_{0.5}^{2.5} B \cdot dA \]Where \( dA \) is the differential element of the area in the appropriate direction.**Detailed Solution:**For deeper insight and the detailed step-by-step solution, refer to the section on magnetic flux in cylindrical coordinates.

Answered: ()* crossing the plane surface given by…

()* crossing the plane surface given by 0.5 ≤rs 2.5m and 0szs 2.0m. Q.4: In cylindrical coordinates, B= T. Determine the magnetic flux

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Electric field

A physical field present around an electrically charged particle that exerts a force on all other charged particles is called an electric field. The charged particles present in the field either repel or attract. From electric charges or time-varying magnetic fields, the electric field originates. One of the manifestations of electromagnetic force which is one of the four fundamental forces present in nature are the electric fields and magnetic fields.

Question

### Magnetic Flux in Cylindrical Coordinates

**Problem Statement:**
In cylindrical coordinates, the magnetic field is given by:
\[ B = \left( \frac{4}{r} \right) \hat{\phi} \text{ T} \]

Determine the magnetic flux \(\Phi\) crossing the plane surface given by:
\[ 0.5 \leq r \leq 2.5 \, \text{m} \]
and
\[ 0 \leq z \leq 2.0 \, \text{m} \]

**Steps to Solve:**
1. Identify the bounds of the integration in \(r\) and \(z\).
2. Recognize that the magnetic field is radially dependent, and it's directed along the \(\hat{\phi}\) direction.
3. Integrate the magnetic field over the specified surface area to find the magnetic flux \(\Phi\).

**Explanation:**
- In cylindrical coordinates, the given magnetic field varies with \(r\) and is independent of \(z\) and \(\phi\).
- The problem encompasses integrating over the surface bounded in \(r\) from 0.5 m to 2.5 m and in \(z\) from 0 m to 2 m.

Understanding this problem involves calculating the magnetic flux by setting up appropriate integrals over the defined bounds. The magnetic field component in the \(\hat{\phi}\) direction and its dependence on \(r\) must be considered carefully while performing the integration.

**Example of Integral Setup:**
\[ \Phi = \int_{0}^{2.0} \int_{0.5}^{2.5} B \cdot dA \]
Where \( dA \) is the differential element of the area in the appropriate direction.

**Detailed Solution:**
For deeper insight and the detailed step-by-step solution, refer to the section on magnetic flux in cylindrical coordinates.

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